I don't think induction is necessary. To show that this is always positive, show that the numerator and denominator are always the same sign (I can't see any reason why either of them would ever be negative...)

Always using n --> n+1, made me forget that n+1 --> n+2 is also allowed. Thanks

You can use any two consecutive general terms. The point is to show by the base step that you knock over the first domino, and by the inductive step that knocking over any domino will knock over the next one.